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Numerical and Analytical Investigation of the Dynamics of a Body Under the Action of a Periodic Piecewise Constant External Force

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Mathematical Modeling and Supercomputer Technologies (MMST 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1750))

Abstract

The paper investigates the dynamics of a body under the action of a piecewise constant periodic force with an arbitrary duty cycle and an oscillation limiter. Analytical relations for point mappings are presented for the first time using the Poincaré point mapping method. These relations allow one to study arbitrarily complex periodic motions both with a finite and infinite number of fixed points on the Poincaré surfaces. As a result, exact equations are presented in an analytical form that determine in the parameter space the existence and stability domains of periodic motions with an infinite number of fixed points on the Poincaré surfaces. The constructed with the help of a software product developed in the C++ language, bifurcation diagrams demonstrate, for some parameter values, the existence of chaotic regimes of body motion. Thus, the scenario for chaos origin is given. The comparison of numerical and analytical calculations is presented for different sets of parameters of the dynamical system.

Supported by organization National Research Lobachevsky State University of Nizhny Novgorod.

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Acknowledgements

The work was carried out with the financial support of the Ministry of Science and Higher Education of the Russian Federation (task 0729-2020-0054).

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Authors and Affiliations

  1. Lobachevsky University, Gagarin Avenue, 23 bld, 603022, Nizhny Novgorod, Russia

    Irina V. Nikiforova, Vladimir S. Metrikin & Leonid A. Igumnov

Authors
  1. Irina V. Nikiforova
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  2. Vladimir S. Metrikin
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  3. Leonid A. Igumnov
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Correspondence to Irina V. Nikiforova .

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Editors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Dmitry Balandin

  2. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Konstantin Barkalov

  3. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Iosif Meyerov

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Nikiforova, I.V., Metrikin, V.S., Igumnov, L.A. (2022). Numerical and Analytical Investigation of the Dynamics of a Body Under the Action of a Periodic Piecewise Constant External Force. In: Balandin, D., Barkalov, K., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2022. Communications in Computer and Information Science, vol 1750. Springer, Cham. https://doi.org/10.1007/978-3-031-24145-1_6

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  • DOI: https://doi.org/10.1007/978-3-031-24145-1_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-24144-4

  • Online ISBN: 978-3-031-24145-1

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